METHOD OF COUPLED CONTROL OF WATER FLOW RATES OF ALL SHOWERS IN SECONDARY COOLING PHASE OF CONTINUOUS CASTING AND SYNTHESIS OF CONTROLLER THEREOF

Abstract

A mehtod for maintaining steady temperatures at longitudinally placed control points along the strand in a continuous casting process, the mehtod comprising: - providing atleast one fuzzy logic controller (3); - selecting atleast two input data (Input - 1, Input - 2) for feeding into the fuzzy logic controller (3); - providing a heat transfer module (1); - feeding one of a stored and an on-line data representing a casting condition and an initiating shower flow-rates to the heat transfer module (1) for generating temperatures at all grid points; - providing a FLC-input-extractor module (2) which acquires the at least two input data (Input - 1, Input - 2) at the desired control locations for feeding the data to the fuzzy logic controller (3); - issuing change-commands signals via the fuzzy logic controller (FLC) in respect of the shower-flow-rates based on data received from the heat trasfer module (1) and the FLC-input-extractor module (2), and - inserting the changed-data in the heat transfer module (1) to generate outputs at the next simulation step.

Full Text

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FIELD OF THE INVENTION
The invention generally relates to a cooling device used in a continuous casting process in the Foundry. More particularly, the invention relates to a method for maintaining steady temperatures at longitudinally placed control points along the strand in a continuous casting process. The present invention further relates to a method of synthesizing in a general algorithm (GA) an association matrix in the fuzzy logic controller to achieve optimal performance in carrying-out the method.
BACKGROUND OF THE INVENTION
Continuous slab casting is a process where liquid steel is continuously poured into a copper mould to construct the slabs. The solidification process initiates at the top most level of the liquid steel (the meniscus) within the mould cavity and it propagates as the solidifying strand descends down. The copper mould is cooled by running water. The mould cooling must be sufficient to strengthen the shells towards withstanding the ferro-static pressure of the liquid core. This stage of cooling is called primary cooling.
Beneath the mould the solidifying strand travels through banks of nozzle showers (sprays) where jets of air-water mixture are impinged on the strand surface. The purpose of this cooling zone is to continue the heat extraction and the solidification that are initiated in the mould, but at a greater intensity. The cooling strategy in this zone should be so designed that the solidification should

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complete within this zone and as such without generating tensile stresses of sufficient magnitude to cause internal defects and cracks. This stage of cooling is called secondary cooling. Figure 2, provides a schematic view of primary and secondary cooling processes in continuous casting.
The strand is further air cooled in the radiation zone, which follows the spray cooling zone and precedes the torch-cutting machine. In the torch-cutting machine the completely solidified strand is cut to slab-sizes and the slabs are fed to the mill.
The heat extraction of the solidifying strands plays a major role in producing quality slabs. In the primary cooling stage, inadequate cooling may develop thinner shell and as a consequence may lead to rupture or breakout of the shell, Excess cooling, on the other hand, may lead to shape deformation or crack formation.
In the secondary cooling zone uneven cooling may cause bulging of strands or propagate cracks that are initiated in the mould. Severe bulging may lead to breakage of the strand. Continuous occurrence of bulging and squeezing of strand within the roll gaps can lead to mould level fluctuations.
Within the framework of the machinery and processes related to the solidification of steel slabs generated during the continuous casting process of the steel making process chain, secondary cooling is enforced to cool the strand consisting of solid shell and liquid interior such that the latter solidifies completely.

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The secondary cooling is controlled by using the casting speed to determine the flowrate of all showers through direct variation law.
This form of control fails to ensure steady temperatures at different longitudinal distances from strand meniscus, particularly under conditions of major changes in casting speed, whereas steady temperatures are highly desirable from the viewpoint of metallurgical quality.
In a real-time control framework the deviation between desired and actual temperatures at a longitudinal control point that controls a shower actually modifies the flow rate of that shower only at the next time instant, however, simultaneously all other showers would also have to be modified under impulse of the temperature deviations at their respective control points.
If each control point-shower flow pair were left independent of the others this would trigger a chain of zig - zag responses for each shower flow rate, in other words the shower flow modulations needs to be coupled across all the showers.
The critical elements for configuration of a fuzzy logic controller are the input and output subsets of each of the variables, and the fuzzy associative matrix or FAM, because the performance of the controller being dependent on the design of these features. Thus, it is necessary to contemplate such a configuration to improve the performance of a fuzzy logic controller.

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The prior art configurations related to spray or shower water are generally developed in experimental scale. Such devices implicitly assume that the caster operates at steady state and most of their empirical formulations are applied only in this condition. In reality, steady state in casting speed is rarely achieved. This is due to the operational practices such as start-up; capping off; ladle, tundish or shroud changes; or due to unplanned events such as nozzle blockage.
As the speed changes of the caster is unavoidable, the problem persists as to the adjustment of shower flows corresponding to the speed changes. Common practice is to vary the shower water rate throughout the secondary zone in direct proportion to the casting speed changes. The proportional constants are empirically developed. This cooling methodology adopted by many steel plants. Although the methodology is simple but is incompatible with the nature of slab cooing within the continuous casting framework, and hence leads to inferior quality slabs.
OBJECTS OF THE INVENTION
It is therefore an object of the invention to propose a method for maintaining steady temperatures at longitudinally placed control points along the strand in a continuous casting process which neutralizes the deviation between the desired and actual temperatures at each longitudinal control point.
Another object of the invention is to propose a method for maintaining steady temperatures at longitudinally placed control points along the strand in a continuous casting process which selects the inputs of the fuzzy logic controller for each shower enabling automatic coupling with its upstream showers.

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An yet another object of the invention is to propose a method for maintaining steady temperatures at longitudinally placed control points along the strand in a continuous casting process in which the subsets are selected heuristically but the matrix elements in the fuzzy logic controller are selected to achieve optimum performance of the controller by adapting a genetic algorithm.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
Figure 1 - Schematic of a control and synthesis method.
Figure 2 - Schematic of a typical continuous casting and cooling processes in a water-cooled copper mold.
Figure 3 - Data relating to Variation of fixed-location temperatures with casting speed according to the invention.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION
The present invention basically comprises two aspects. In one aspect of the invention a fuzzy logic controller is provided for maintaining steady temperatures at longitudinally placed control points along the strand by modulating all shower flow rates in coupled mode. In a second aspect of the invention, a synthesis method is provided for optimizing the operation of the fuzzy logic controller using genetic algorithms and offline simulations.

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A fuzzy logic controller (FLC) is provided that takes inputs and generates output, the output being a commanded change in shower flow rate for a specific shower which the fuzzy logic controller (FLC) is controlling i.e. a percentage value. The inputs provided to the fuzzy logic controller (FLC), is selected such that it is able to maintain consistent temperatures and integrate with the outputs of its upstream showers.
The following inputs are taken:

T stands for temperature and the subscripts are self-explanatory. The temperatures are considered at a representative control point on the strand which controls a specific shower. Thus there is a one-to-one relationship between a shower and its control point, or vice versa.
For Input 1, the Terror is the parameter desired to be minimized. If a mold is provided with N showers with N control points, only Input 1 is used. At the Kth discrete time step at the jth shower (and control point), Input 1 at control point j commands (through an FLC) a certain change in flow rate of shower j. Such a command is effected only at time step k+1. At the time-step k, the control point j-1 is transmitted which too is effected at the time step k+1. Such a phenomenon implies that at the instant of command effectiveness, i.e. k+1, the Input 1 at control point j has already shifted due the change effected at shower

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j-1 commanded at time step k, and due to the downward propagation of influence. At the shop-floor level implementation, it has been found that when the Terror is 0 (deg.) and Terror-at-upstream-shower is +30, the considered shower satisfactory performs and no change is envisaged. When a +(ve) Terror is captured due to insufficient cooling by the controller causes the flow rate of the upstream shower to increase so that Terror-at-upstream-shower becomes 1, but the cooling of the downstream shower does not change the temperature at its own control point. As a result, 20 deg. Lower temperature than earlier is transmitted at its upstream point, and hence Terror at downstream point shifts from 0 to -20. Obviously, Input is alone not sufficient and Input 2 needs to be further considered, which pre-empts the direction of change induced on the downstream control point by the upstream shower and make the downstream shower react accordingly.
Furthermore, with inclusion of Input 2 for each shower's FLC, the upstream shower is also modified to balance changes in its own upstream shower flow rate, and thus, the effect of all upstream showers are incorporated at a given longitudinal control point-hence cross-shower coupling can be achieved.
Thus, according to the first aspect of the invention, selection of an input data in a fuzzy control which provides a coupled nonlinear control of the secondary cooling, is made.
Although the data related to Tdesired is obtainable from metallurgical principles, Terror is obtained online, in real time. A CFD-based heat transfer module is

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implemented for the purpose. The data considered in developing the program are the casting speed, superheat, chemical composition of the casting material, and heat removal in primary cooling which provides converged solution in the form of a temperature distribution all along the strand surface in real-time.
The second aspect of the invention relates to a method of synthesis of the Fuzzy controller logic (FLC). Figure 1 shows a synthesis method which is based on genetic algorithm.
The steps followed in the generic algorithm constitute selection, crossover and mutation. Starting with the population of strings representing codified solution vectors from the total solution space, a selection step creates a new generation of population by randomly selecting strings from the current generation, and assigning weights to the fitness value of each string. Strings with higher weights are likely to get more copies in the new generation, and those with low fitness might be eliminated, the word 'might' signifying the probabilistic nature of the generic algorithm (GA). A step of Crossover takes up pairs of strings and switches the bits lying on one side of a particular common 'crossover point'. A step of Mutation flips individual bits of a string periodically based on a probability of mutation. The step of crossover leads to creation of new solutions, while mutation allows the solution to jump from one point of the solution space to another. Together, all three operations complementarily guide the GA process towards the optimal solution with highest fitness.

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In the present invention each candidate solution constitutes a possible combination of elements of the fuzzy associated matrix (FAM) for the fuzzy logic controller (FLC). A simulation of the secondary cooling process is performed to evaluate the FAM performance as the controller.
The starting box shown in Figure - 1 at top left, brings in the casting conditions. Instead of streaming data as characteristic of online conditions, stored data can be used. Each stored data feeds casting condition data, along with initiating shower flow rates, to the Heat Transfer module. The module generates temperatures at all grid points. Then an FLC-input-extractor module acquires Inputs 1 and 2 at the desired control locations and feeds it to the FLC, one for each shower/control-point. The FLC commands changes in shower flow rates. The changes rates are then inserted to the Heat-Transfer module to generate its outputs at the next simulated time step, and the process continues.
At each simulated time step, the square of Terror at each control point is recorded. These are summed for each control point at a time step, and at all time steps till the selected casting condition data files are exhausted. The net summed value (see figure 2) is the fitness of that FLC. In this way, at each GA generation the fitness is evaluated for each candidate solution, till the GA converges to the best solution, i. e. best FAM and hence best FLC.
Figure 2 shows a casting mould (M). The molten material in the form of solidifying strand (SS) traveling through a plurality of nozzle showers (Sn) spraying air-water mixture on the surface of the solidifying strand (SS) in a secondary zone (SZ) for extraction of heat. The solidification process initially

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originates within the mould (M) where the mould (M) is cooled by running water thereby strengthening the core of the liquid melt in a primary zone (PZ). The strand (SS) is thereafter air-cooled in a radiation zone (RZ). A plurality of rollers (Rn) is disposed to ease the travel of the liquid molten metal including the solidifying strand.
In Figure 3, casting speed in meters / min is shown in the right y-axis, and temperatures in degrees Celsius is shown in the left-axis. A time span of 3 hours is shown. Temperatures are recorded by infra-red cameras at three longitudinal locations, it is easily seen that they all end up tracking the casting speed with a lag.

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We Claim
1. A method for maintaining steady temperatures at longitudinally placed control points along the strand in a continuous casting process, the method comprising:
- providing atleast one fuzzy logic controller (3);
- selecting atleast two input data (Input - 1, Input - 2) for feeding
into the fuzzy logic controller (3);
- providing a heat transfer module (1);
- feeding one of a stored and an on-line data representing a casting
condition and an initiating shower flow-rates to the heat transfer
module (1) for generating temperatures at all grid points;
- providing a FLC-input-extractor module (2) which acquires the at
least two input data (Input - 1, Input - 2) at the desired control
locations for feeding the data to the fuzzy logic controller (3);
- issuing change-commands signals via the fuzzy logic controller
(FLC) in respect of the shower-flow-rates based on data received
from the heat transfer module (1) and the FLC-input-extractor
module (2), and

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- inserting the changed-data in the heat transfer module (1) to
generate outputs at the next simulation step.
2. The method as claimed in claim 1, wherein the input data (Input - 1,
Input - 2) comprises:
Input 1: Terror = Tactual - Tdesired
Input 2: ?Terror = Terror - Terror-at-upstream-shower
the T being the temperature at respective control points on the solidifying strand (SS).
3. A method of synthesis in a genitic algorithm (GA) an associative matrix in
the fuzzy logic controller to achieve optimal performance in carrying-out
the method as claimed in claims 1 to 2, the method comprising the steps
of:
- creating a new generation of population of strings by randomly
selecting from the current generation, the population of strings
representing codified solution vectors from a total solution space;
- assigning weights to the fitness value of each string leading to
inclusion of the majority of the strings of higher fitness in the
created new generation;

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- selecting the strings in pairs and switching the bits lying on one
side of a particular common cross-over point leading to creation of
new solutions;
- periodically flipping individual bits of a string based on a probability
of mutation allowing a solution to jump from one point of the
solution space to another;
- each candidate solution so determined constituting a most
probabilistic elements of the associated matrix in the fuzzy logic
controller (FLC), the candidate solution being further confirmed by
performing an on-line simulation of the cooling step in the
secondary zone (SZ).

4. A method for maintaining steady temperatures at longitudinally placed
control points along the strand in a continuous casting process as
substantially described herein with reference to the accompanying
drawings.
5. A method of synthesis in a genitic algorithm (GA) an associative matrix in
the fuzzy logic controller to achieve optimal performance in carrying-out
the method as substantially described herein with reference to the
accompanying drawings.